BOUNDEDNESS OF VOLTERRATYPE OPERATOR ON ANALYTIC MORREY SPACE

• Main Author: Taufik Hakiki, Moch.
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/49710
• Institution: Institut Teknologi Bandung

The Volterra operator is one of many important integral operator in functional analysis and operator theory. Volterra operator was first studied on Hilbert spaces L2[a, b] and by the time, Volterra operator has been considered on various function spaces. This thesis studies an integral operator Tg defined on spaces of analytic function on the unit disc D. The operator Tg with symbol g(z) of analytic function on the unit disc, is defined by Tgf(z) = R z 0 f(w)g?(w) dw. This operator generalized the Volterra operator, that is, when g(z) = z. In addition, another integral operator Ig defined as Igf(z) = R z 0 f?(w)g(w) dw and the multiplication operator Mgf(z) = f(z)g(z) are considered. The main purpose of this thesis is to find the characterization of an analytic function g such that the integral operaor Tg and Ig are bounded on analytic Morrey spaces. The analytic Morrey spaces could be viewed as a complex version of the classical Morrey spaces. Furthermore, estimation of the opertaor norm Tg and g are studied. The results of this thesis is then compared with some previous related results about the characterization of operator Tg and Ig on analytic function spaces.